Physical and statistical challenges to model and simulate climate extremes Pascal Yiou, Camille Cadiou, George Miloshevich, Robin Noyelle, Flavio Pons LSCE, IPSL Séminaire S3 1

Motivation • More frequent? • More intense? • Role of human activities? • What actions? What uncertainties? Séminaire S3 2

Extreme Event Attribution (EEA) Consider a given extreme event (heatwave, cold spell, intense precipitation…) • Estimate the change of probability distribution of exceeding an observation, between a factual and counter factual world • Factual = present-day climate/environment • Counter factual = world that could be/was without human intervention • Design a narrative (or storyline) of a similar extreme, with exacerbated components, in factual and counter factual worlds Séminaire S3 3

General Simulation Framework Hypotheses • We have a physical system (𝑋) with complex dynamics (e.g. climate system) • We have (partial, finite, etc.) observations of 𝑋: 𝑓(𝑋(𝑡)) • The observed record value of observations 𝑓(𝑋 𝑡 ) is & 𝑀! . Questions • How to obtain the maximum possible (unobserved) value of 𝑓(𝑋)? • What are the precursors of & 𝑀! ? • Is & 𝑀! affected by climate change? (and how?) Séminaire S3 4

Climate Framework & Motivation • The 2003 European heatwave had a probability < 10"# and is still the record for JJA temperature • Studying the physical properties of such an event require a fairly large sample of similar events (>1000 years) • There are no observational records that are long enough to provide enough samples • Such events can be outliers for Extreme Value Theory! (“Black Swans”) • Fischer et al. (Nature Comm. 2023) Séminaire S3 5

Simulation of rare/extreme events • Model or Dynamical system 𝑋(𝑡) : $! $% = 𝐹(𝑋) • Chaotic, multivariate, high-dimensional… • Scalar observable 𝑇(𝑡) of the system 𝑋 𝑡 : • 𝑇 𝑡 = 𝑓(𝑋 𝑡 ) • How to simulate trajectories of 𝑋 that maximize 𝑇 & = ∫ ' & 𝑇 𝑡 𝑑𝑡 over a given period 𝑃 of time? • max 𝑇 ! ? (e.g. max average summer temperature: 𝑃 = 90 days) • Simulate trajectories of 𝑋 for which ℙ 𝑇 ! > 𝑇"#$" > 𝛼"#$" Séminaire S3 6

Forecast/Anticipate/Attribute Extreme Events The system 𝑋(𝑡) reaches an extreme state 𝒜 : • ℙ 𝑋 𝑡 ∈ 𝒜 = 𝑝𝒜 ≪ 10&' 𝑝𝒜 could be very hard to estimate due to the lack of data • Challenge 1: What is 𝒜 for 0 < 𝑝𝒜 ≪ 10")? • Challenge 2: Estimate conditional forecast probabilities when 𝒜 is known • 𝑝((𝜏) = ℙ 𝑋 𝑡 + 𝜏 ∈ 𝒜| 𝑋(𝑡) Séminaire S3 7

Challenge 1: What is 𝒜 for 0 < 𝑝𝒜 ≪ 10"#? • Rare event algorithms: • Simulate rare trajectories of 𝑋 leading to an extreme • Examples: simulate extremely hot summers or extremely cold winters (e.g., Ragone et al. PNAS 2017) • General framework(s): • Large deviation theory (e.g., Lucarini et al. ERL 2023) • Ensemble boosting (e.g. Gessner et al. J. Clim. 2021) • Requirements: • Models (physical or statistical) • End uses: • Anticipation of worst case scenarios, e.g. storylines (Sillmann et al., Earth’s Future, 2021) • Does climate change affect the properties of 𝒜 ? (Attribution of extremes) Séminaire S3 8

Challenge 2: Estimate 𝑝$ (𝜏) • Simulations of 𝑋(𝑡) for various initial conditions (Ragone et al., PNAS, 2017) • General framework: • Ensemble forecast of climate variables • End uses: • Identify conditions where 𝑝( 𝜏 > 𝑝) ≫ 𝑝𝒜 (i.e. precursors of 𝒜) • Forecast of extremes (Miloshevich et al., 2023) • Are those conditions affected by climate change? • Attribution of extreme Séminaire S3 9

A Cost Effective Framework • Analogs of circulation to simulate temperatures in the mid latitudes • Stochastic Weather Generator (SWG) as a climate emulator for extremes • How to address the challenges of simulating worst cases and the impact of climate change? • Focus on case studies • Paris Olympics in 2024 • A worst case cold winter (1962/1963) Séminaire S3 10

Analogs and Importance Sampling • Adapting Analog Stochastic Weather Generator (Yiou, GMD, 2014) to maximize summer temperature (Yiou and Jézéquel, GMD, 2021) • Reshuffling analogs of circulation with weights towards highest temperatures • Synonyms for analogs: • Recurrences (Poincaré + Freitas et al. Th.) • K-nearest neighbors • Use for ensemble weather forecast (another seminar) Séminaire S3 11

Day d, Year y d,y d±30,y’≠y Climate observable (Temperature) Corresponding circulation (Z500 detrended) N best analogues 1 2 N N 2 1 Similar to ? Procedure of analogues Séminaire S3 12 (Jézéquel et al., Clim. Dyn., 2018)

Analog Stochastic Weather Generator Random selection of Z500 analogs (among 𝐾 = 20 analogs), with weights that are proportional to the rank of the corresponding day temperature: 𝑤! = exp( −𝛼" rank(𝑇!)) Weights on the distance to the calendar day to be simulated 𝑤! = exp(−𝛼#$% |𝑡! − 𝑡|) Simulation of ensembles of trajectories that optimize average temperature (e.g. during a season, JJA) Return period of ensemble is proportional to 𝜶 Séminaire S3 13 (Yiou and Jézéquel, Geophys. Mod. Dev., 2021)

Importance sampling with SWG Séminaire S3 14

Analog Stochastic Weather Generator • The analog SWG is a Markov chain of temperatures with latent states (large-scale atmospheric circulation: Z500) • The rare event algorithm (importance sampling) modifies the probabilistic properties of the ”basic” Markov chain (when 𝛼 = 0) in order to sample realistic trajectories that lead to high temperatures • Its range of application is for ”long lasting” events (months, seasons) • The integration time of trajectories has to be large with respect to the integration time step • Same constraint as in Ragone et al. (PNAS, 2017) Séminaire S3 15

Features & challenges • Variation of a Darwinian mechanism • favor the strongest (Yiou and Jézéquel 2019) vs. eliminate the weakest (Ragone et al. 2017) • Parameters to be optimized! • Large-scale predictors in analog pre-computation (Z500, Z500 & RH?, Z500 & SLP?) • Which region? • How to use climate model simulations, e.g. for future climates? • What “observable” to consider, especially for compound events? Séminaire S3 16

Simulating worst case heatwaves during the Paris 2024 Olympics Pascal Yiou With: C. Cadiou, D. Faranda, A. Jézéquel, N. Malhomme, G. Miloshevich, R. Noyelle, F. Pons, Y. Robin, M. Vrac LSCE, LMD & IPSL Séminaire S3 17 Yiou et al. npj Climate and Atmospheric Science, https://doi.org/10.1038/s41612-023-00500-5

Challenge: Paris Olympics 2024 • Paris 2024: 26/07 to 11/08 2024 • Apex of the temperature seasonal cycle • Can the record shattering event of 2003 be broken in 2024? • Consider TG15d in JJA (max of T15d in JJA) • Four SSP scenarios of CMIP6 (2015-2050) + historical (1950-2014) simulations, with R2D2 bias correction Séminaire S3 18

Years TG15d [°C] 18 22 26 30 1940 1960 1980 2000 2020 2040 2060 2003 18 22 26 30 historical SSP1−2.6 SSP2−4.5 SSP3−7.0 SSP5−8.5 (a) IPSL TG15d [°C] 18 24 30 ERA5 AS−RCEC BCC CCCma CMCC CNRM−CERFACS CSIRO EC−Earth−Consortium IPSL MIROC MPI−M MRI NCAR NCC NOAA−GFDL (b) Séminaire S3 19 TG15d in ü historical, ü SSP1-2.6, 2-4.5, 3-7.0 and 5-8.5 simulations of IPSL-CM6-LR TG15d in ERA5 TG15d during preceding Olympics Boxplots of TG15d of Ile de France in CMIP6 with R2D2 (*) bias correction (*) Vrac, M., and S. Thao, Geophys. Mod. Dev., 2020 Data: TG15d in Ile de France

SWG simulations based on IPSL model TG15d [°C] 18 20 22 24 26 28 30 32 1951−2000 2001−2050 ssp126 (a) Days TG [°C] (b) ssp126 5 10 15 18 20 22 24 26 28 30 32 max(TG15d) q50 SWG [1951−2000] q50 SWG [2001−2050] q05−q95 SWG TG15d [°C] 18 20 22 24 26 28 30 32 1951−2000 2001−2050 ssp245 (c) Days TG [°C] (d) ssp245 5 10 15 18 20 22 24 26 28 30 32 TG15d [°C] 18 20 22 24 26 28 30 32 1951−2000 2001−2050 ssp370 (e) Days TG [°C] (f) ssp370 5 10 15 18 20 22 24 26 28 30 32 TG15d [°C] 18 20 22 24 26 28 30 32 1951−2000 2001−2050 ssp585 (g) Days TG [°C] (h) ssp585 5 10 15 18 20 22 24 26 28 30 32 Séminaire S3 20 Step 1: Find the highest TG15d in 2001- 2050 (and its first day) Step 2: Simulations start on the highest TG15d of IPSL-CM6-LR with analogs in 1951-2000 and 2001-2050 2003 record exceeded in 3 SSP scenarios

SLP composite patterns Séminaire S3 21 Composites of SLP for identified records of TG15d (between 2001 and 2050) Composites of SLP for SWG simulations with analogs in 1951-2000 and 2001-2050 Anticyclonic conditions + cut-off low?

Cold winters in Europe −6 −4 −2 0 2 4 6 8 1950 1960 1970 1980 1990 2000 2010 2020 Year Temperature (°C) 3 10 30 90 (a) −4 −2 0 2 4 6 8 10 Dec Jan Feb Date Temperature (°C) 1951−2021 1956 1963 1985 1987 Seasonal mean (b) Séminaire S3 22 Dependence on time scale (from 3 days to whole winter) Impacts on the energy & health sectors Record breaking cold winter in 1962/1963 • a record shattering event: more than 2𝜎 colder than average • Several cold spells during the winter In spite of the increasing temperature, can such a cold winter be reached? Cadiou and Yiou (2023)

The Cold Winter of 1962/1963 Séminaire S3 23 Sippel et al. (2023) How cold would be a winter with a similar atmospheric circulation in present-day climate? Strategy • Simulate a climate model with initial conditions close to Dec. 1st 1962 • CESM2 (ETH Zurich): boosting by selecting cold trajectories • SWG (IPSL)

How cold can it get? ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● −6 −4 −2 0 2 4 6 8 1951−1999 1972−2021 TG90d (°C) (a) −6 −4 −2 0 2 4 6 8 Dec Jan Feb Mar TG (°C) (b) Séminaire S3 24 Ensembles of SWG simulations with analogs in 1951-1999 and 1972-2021 1962/1963 Barely no increase of 𝑇 &'( between the two periods, in spite of an increase of the mean Breaking the 1962/1963 record is (still) possible when no information on that winter is included

SWG Circulation patterns Séminaire S3 25 • Analogs of Z500 in ERA5 in 1951-1999 and 1972-2021 • Low Z500 anomaly over France, anticyclonic anomaly over Ireland • Advection of cold air from Scandinavia or Siberia DJF 1962-1963

Simulating the coldest winters in Germany Séminaire S3 26 Sippel et al. (Wea. Clim. Dyn. discuss. 2023) Model boosting “à la” ETH Zurich (Gessner et al., J. Clim. 2021): • Start on Dec. 1st 1962 • 900 simulations of 90 days • 2nd boosting in Jan. 1963: restart from the coldest simulation (strong convergence to seasonal cycle) Colder winters than 1963 are possible in present day climate with CESM2 boosting and SWG simulations (based on ERA5)

Conclusions An application of statistical mechanics methods to climate sciences to investigate worst cases • Heatwave during the Olympics? • Forecast • Anticipation • Attribution: 2003 record can be exceeded with analogs in 2001-2050, hardly with analogs in 1950-2000. • A record breaking cold winter in Europe in 2024? • Lower probability than in the 20th century BUT still possible • December 1962 initial conditions can lead to such cold winters Perspectives? • Can heatwaves be predicted: Estimation of committor function from SWG (G. Miloshevich): • How to reach the upper bound of daily temperature (Noyelle et al. Envir. Res. Lett. 2023) Séminaire S3 27